The fine print.
Participants in this seminar are expected to attend regularly, read the
assigned readings and take their turn in presenting material. The final
grade is based on these presentations and on an essay to be submitted
on Friday April 23 in 1017CL by 4:45 pm. My policy is NOT to issue
incomplete grades, excepting in extraordinary circumstances. I really
do want your essays completed and submitted by the end of term. I do
not want them to linger on like an overdue dental checkup, filling your
lives with unnecessary worry and guilt. In return for the rigidity of
the deadline, the seminar will not meet in the final week of term
(Tuesday April 20). The essay may be on any subject of relevance to the
seminar. To assist you in commencing work, I ask you submit an essay
proposal to me by Tuesday March 23. The proposal need only be brief. It
should contain a short paragraph describing the topic to be
investigated and give a brief indication of the sources you intend to
use. Do talk to me about possible topics!

Einstein's corpus of 1905

This seminar will center on the reading of Einstein's papers of 1905, his annus mirabilis, and their interpretation in the history of science literature. The papers comprising the corpus are:

This is Einstein's doctoral dissertation, submitted after much delay to
the University of Zurich. In it he uses available physical data on the
diffusion of sugar in solution and the effect of dissolved sugar on the
solution's viscosity to determine the size of sugar molecules and
Avogadro's number. The analysis makes the kinetic theory of heat more
definite, in so far as it provides a measure of the real size of
molecules, so that they cannot be dismissed as easily as useful
fictions. It is the least impressive of Einstein's work of 1905
although, curiously, the most cited.

"On the motion of small particles
suspended in liquids at rest required by the molecular-kinetic theory
of heat." (Brownian motion paper) (May 1905; received 11 May 1905)Annalen der Physik, 17(1905), pp. 549-560.

In this paper Einstein reports that the kinetic theory of heat predicts
that small particles suspended in water must execute a random motion
visible under the microscope. He suspects this motion is Brownian
motion but has insufficient data to affirm it. The prediction is a
powerful test of the truth of the kinetic theory of heat. A failure to
observe the effect would refute the theory. If it is seen and measured,
it provides a way to estimate Avogadro's number. The domain in which
the effect is observed is one in which the second law of thermodynamics
no longer holds, a disturbing result for the energeticists of the time.

Einstein develops the special theory of relativity in this
paper. His concern, as he makes clear in the introduction, is that then
current electrodynamics harbors a state of rest, the ether state of
rest, and the theory gives very different accounts of electrodynamic
processes at rest or moving in the ether. But experiments in
electrodynamics and optic have provided no way to determine which is
the ether state of rest of all inertial state of motion. Einstein shows
that Maxwell-Lorentz electrodynamics has in fact always obeyed a
principle of relativity of inertial motion. We just failed to notice it
since we tacitly thought that space and time had Newtonian properties,
not those of special relativity.

While the victory in the 19th century of the electromagnetic wave
theory of light over Newton's corpuscle view is undeniable, Einstein
shows that its success is incomplete. The theory gives incorrect
results for the analysis of heat radiation. He looks at the
thermodynamic properties of high frequency heat radiation and finds
that this radiation behaves just like a collection of many spatially
localized units ("quanta") of energy of magnitude hf (h=Planck's
constant, f=frequency). He proceeds to show how this quantum view of
light makes sense of several experiments in electrodynamics and optics,
the best know being the photoelectric effect. He then described the
paper as "revolutionary."

Advance work.

Here is what I want you to do prior to my presentation on each of these papers.

Read the paper. Einstein is using known properties of sugar
solutions to fix values for the size of sugar molecules P and
Avogadro's number N. One might have hoped that data on diffusion of
sugar alone might be sufficient. But it turns out to give an expression
for NP only. Einstein needs a second relation between N and P to
recover individual values. He arrives at it from his analysis of the
effect of solutes on the viscosity of a solution. The analysis is in
Sections 1-2. It is very tough going and should be skimmed (on a first
read). The conlcusion that matters is stated in the last paragraph of
Section 2. "If very small spheres are suspended in a liquid, ..."

What is Stokes' law? Under what conditions does it obtain?
What is osmotic pressure?What law relates osmotic pressure to temperature?
How is the coefficient of diffusion defined?

What is Einstein's stated purpose?
Find two approximations used in his calculations. Are the approximations licit?

"On the motion of small particles suspended in liquids at rest
required by the molecular-kinetic theory of heat." (Brownian motion
paper)

Read the paper. The central results of the paper are in Sections 4-5.
In Section 4, a stochastic model of Brownian motion is used to generate
the expression for the root mean square displacement of particles. In
Section 5, the expected magnitude of the motion is computed from values
of the size of particles and Avogadro's number. Sections 1-3 play the
supporting role of generating an expression for the diffusion
coefficient used in Sections 4-5 in terms of Avogadro's number and
particle size. The analysis of Section 2 is independently noteworthy in
that it reveal the extremely general statistcal mechanical basis of the
ideal gas law and its reappearance as the law governing partial
pressures in dilue solutions. (The analysis is very similar to the core
argument of the light quantum paper.)

What is Brownian motion?
What is free energy? How is it used to express the condition of thermal
equilibrium for a system maintained at constant temperature? How can it
be used to recover an expression for the pressure of a thermodynamic
system?
What is the diffusion equation? What are its typical solutions?

How does the Brownian motion paper build on and improve the analysis of Einstein's dissertation?

"On the electrodynamics of moving bodies" (special relativity)

Read the paper. The first "kinematical" part contains the developement
of the special theory of relativity as a new theory of space and time.
It is the most celebrated part of the most celebrated scientific paper
of the 20th century and should be studied closely. It is mathematically
easy, excepting a somewhat overcomplicated derivation of the Lorentz
transformation in Section 3. (Almost any other development will give a
simpler derivation.) The second "elctrodynamical" part is tougher
going. In it, Einstein applies the new theory of space and time to
Maxwell's electrodynamics. The principal goal is to show that the
theory already conforms to the principle of relativity, once we
recognize that space and time behave according to special relativity.
The most important calculation is in Section 6 where Einstein shows the
Lorentz covariance of Maxwell's equations and that the electric and
magnetic fields get mixed under transformations between inertial
frames. Note that the E field has components (X,Y,Z) and the H field has components (L,M,N).

The key to special relativity is the relativity of simultaneity. Make
sure you understand the notion, as laid out in Sections 1 and 2 and how
Einstein shows that attending to the relativity of simultaneity in our
measurement operations leads to the relativity of lengths.

The demonstration of the Lorentz covariance of Maxwell's equations of
Section 6 is the most important result of the paper. If you have the
math, reconstruct the proof.

In Section 10, Einstein talks of transverse and longitudinal mass. What
are they? Why do they cause him trouble and what should he have used?

"Does the inertia of a body depend on its energy content?" (E=mc2)

Read the paper. The argument is short and simple, although
slightly complicated by Einstein's use of transverse and longitudinal
mass in electrodynamics. The main thing to see is that the goal is a
relation between inertia and energy for all forms of matter, not just
electromagnetic. The use of electromagnetic theory is merely the path
Einstein takes to the general result.

How does Einstein manage to have his result apply to all forms of matter?

"On a heuristic viewpoint concerning the production and transformation of light." (light quantum/photoelectric effect paper)

Read the paper. The core arguments are in Sections 5 and 6. In Section
5, Einstein gives an especially lucid demonstration of this result: if
a system consists of many, independent energy elements, its entropy
varies with the logarithm of its volume. In section 6, Einstein notes
that the entropy of high frequency radiation does vary logarithmically
with volume so that it has the characteristic fingerprint of a system
of many independent energy elements. The remaining Sections 7-9 give
three experimental demonstrations of the localization of energy in
radiation; the photoelectric effect is the best known. Earlier sections
provide supporting results, including the expression for the entropy of
high frequency radiation. Section 1 contains a lucid demonstration of
the failure of classical physics to accommodate black body radiation.

Find Einstein's complete statement of the light quantum hypothesis in the paper. Note how it is carefully hedged.
Why does Einstein restrict his analysis to high frequency radiation? Does this mean low frequency radiation is not quantized?
If radiation turns out to be quantized, how does Einstein explain the great success of Maxwell's wave theory of light?
Planck, the lore holds, quantized energy in 1900. Is there any evidence
in this paper that Einstein knows this? To what does "quanta" in the
title of Section 2 refer?
Note the similarities between Einstein's argument of Section 5 and his
statistical mechanical derivation of the expression for osmotic
pressure in the Brownian motion paper.

Sources and readings

Einstein's Papers

Contains
facsimiles of the originals of Einstein's papers of 1905 in German.
This is the standard source, with extensive editorial headnotes
introducing the material and footnotes that correct minor errors in the
text and develop background materials. This editorial apparatus
provides the authoritative introduction to Einstein's work of 1905.

An
expansive collection of material on Einstein's paper, the background in
electrodynamics preceding and subsequent developments. The exposition
is not always helpful. Has a translation of the 1905 special relativity
paper.

Edmund Whittaker, A History of the Theories of Aether and Electricity. Dover.

A venerable standard history. Slight idiosyncrasy in attributing special relativity to Lorentz and Poincare.

Stephen G. Brush, The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century. 2 Vols. Amsterdam: North Holland, 1976.
Stephen G. Brush, Statistical Physics and the Atomic Theory of Matter, from Boyle and Newton to Landau and Onsager. Princeton Univ. Press, 1983

Projects

Some suggestions for research projects.

Pais, Subtle is the Lord:... p.89
reports that Einstein's dissertation was his most cited paper in
1970-74. Check whether this is still so and try to come to some
determination over what it tells us about the relative quality and
value of Einstein's papers.

Einstein's methods in his dissertation seem very fragile.
(a) Einstein's entire analysis depends on the assumption that sugar molecules are spheres. They are not.
(b) He recovers the viscosity of a sugar solution by looking at energy
dissipation in one very specialized case of a fluid with spheres. How
can it adequately model a sugar solution? Should we expect that a
fluid, laden with spheres, continues to behave like a Newtonian fluid
for which the ordinary notion of viscosity is applicable?
(c) Einstein's recovers the force on a moving sugar molecule from
Stokes law. But Stokes law was derived for spheres moving uniformly in
a fluid. The motion of sugar molecules in diffusion is not
unidirectional or constant in magnitude.
Yet his results and methods seem to have staying power. How is this possible?

In Australia in 1905, William Sutherland independently discovered
results of Einstein's 1905 dissertation on the diffusion of sugar.
Compare Sutherland's work to Einstein's.

The lore is that a mighty battle was fought over the reality of atoms around 1905. Was it?

Einstein's dissertation and Brownian motion paper was part of a larger
tradition of work on the reality of atoms. Review that tradition,
noting the place of Perrin and the 1911 Solvay conference.

Why did Einstein choose sugar for this dissertation work?

Einstein makes much use of the relation Entropy = k log Probability,
which he calls Boltzmann's principle. The principle must be used with
extreme caution, since it only holds in the right contexts. Investigate
Einstein's use of the principle and grounds for its applicability.

Who discovered Boltzmann's Principle? Boltzmann? Planck? Einstein?

Fluctuation phenomena, such as Brownian motion, demarcated the boundary
of applicability of thermodynamics. How was this threat to
thermodynamics received?

Before his concentration moved to Lorentz's version of Maxwell
electrodynamics, Einstein had studied Hertz' electrodynamics. What
might he have found there of relevance to his discovery of special
relativity.

In his recent book Einstein's Clocks, Poincare's Maps,
Galison describes a similarity between the definition of simultaneity
of the Einstein's 1905 special relativity paper and the method of clock
synchronization used for railroad clocks. Assess the significance of
this similarity.

Einstein's 1905 work on the light quantum was derived from a
statistical mechanical analysis. His 1909 elaboration of wave particle
duality proceeded from an interpretation of the thermal fluctuations of
radiation. How might Einstein's earlier work in the foundations of
statistical physics (1902-1904) have figured in these discoveries?

Kuhn has argued that Planck did not introduce quantum discontinuity in
1900, but that it was really introduced by Einstein in 1905. Assess
this claim.

Schedule of Readings for HPS 2590 Einstein 1905

Date

Reading

Presenter

6 January

Introductory meeting

13 January

The statistical papers: doctoral dissertation

Norton

20 January

Doctoral dissertation.Brownian motion

Norton

27 January

Brownian motion.

Norton

3 February

The light quantum.

Norton

Prize
awarded to anyone who can equal or better my best candidate for an
unexpected use of the statistical mechanical analysis of equilibrium in
a field in Einstein's published papers....and the winner is Alexandre Guay.

Poincare's analysis of clock synchronization. Extracts from The Value of Science

Alexander Afriat

6 April

Einstein's argument in the light quantum paper.
Jon Dorling, "Einstein's Introduction of Photons: Argument by Analogy or Deduction from the Phenomena?" British Journal for the Philosophy of Science, 22 (1971), pp. 1-8.

John Anders

Einstein's use of entropy and S=k log W in the argument for the light quantum.

Wrap up of survey of Einstein's 1905 corpus
John Stachel, "Introduction to Einstein: The Formative Years, pp. 1-22 in Don Howard and John Stachel, eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998.

Norton

(Very unlikely that we have time for it.) Sahotra Sarkar,
"Physical Approximations and Stochastic Processes in Einstein's 1905
Paper on Brownian Motion," pp. 203- 229 in Don Howard and John Stachel,
eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998.

Sahotra Sarkar, "Physical Approximations and Stochastic Processes in
Einstein's 1905 Paper on Brownian Motion," pp. 203- 229 in Don Howard
and John Stachel, eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998.
Juergen Renn, "Einstein's controvery with Drude and the Origin of
Statistical Mechanics: A New Glimpse from the 'Love Letters'," pp.
107-157 in Don Howard and John Stachel, eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998.

Steven Brush, "Brownian Movement," Ch. 15 in The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases in the 19th Century. Vol. 2. Amsterdam: North Holland, 1976.

and more...?

Special relativity

"Einstein on the Theory of Relativity," Papers, Vol. 2, pp. 253-74.

John Stachel, "Einstein and Ether Drift Experiments," pp. 171-76 in John Stachel, Einstein from 'B' to 'Z'.Boston: Birkhaeuser, 2002.

Michel Janssen and John Stachel, "The Optics and Electrodynamics of Moving Bodies," in John Stachel, Going Critical.

John Stachel, "Einstein and Michelson: The Context of Discovery and the Context of Justification," pp. 177-190 in John Stachel, Einstein from 'B' to 'Z'.Boston: Birkhaeuser, 2002.

Robert Rynasiewicz, "The Construction of the Special Theory: Some
Queries and Considerations," pp. 159-201 in Don Howard and John
Stachel, eds., Einstein: The Formative Years, 1879-1909.Boston: Birkhaeuser, 1998.

Michel Janssen, ''The Trouton Experiment, E=mc2, and a Slice of Minkowski Space-Time,'' in John Stachel et al., eds., Revisiting the Foundations of Relativistic Physics: Festschrift in Honor of John Stachel.